Well, the "T B Blues" as recorded by many black artists (I have it done by Memphis Slim) would qualify. Lonnie Johnson's whole family was wiped out by the flu, so he might have recorded something. "Bad Girl's Lament" deals with syphilis. "Arthritis Blues" was sung by Butch Hawes.Lotsa songs in British tradition dealing with "Eel poisoning" [e.g. "Lord Randall"], but that's a bit off track.
Hope this gets the ball rolling. There are some very knowledgeable folks here and you may be surprised just how many "disease songs" there are. Now whether your audience will find them interesting.....?
Rick